Narrow Results

We investigated the motion of two-head Brownian motors by introducing a model in which the two heads coupled through an elastic spring is subjected to a stochastic flashing potential. The ratchet potential felt by the individual head is anti-correlated. The mean velocity was calculated based on Langevin equations. It turns out that we can obtain a unidirectional current. The current is sensitive to the transition rates and neck length and other parameters. The coupling of transition rate and neck length leads to variations both in the values and directions of currency. With a larger neck length, the bi-particle system has a larger velocity in one direction, while with a smaller neck length, it has a smaller velocity in the other direction. This is very likely the case of myosins with a larger neck length and larger velocity in the positive direction of filaments and kinesins with a smaller neck length and smaller velocity in the negative direction of microtubules. We also further investigated how current reversal depended on the neck length and the transition rates.

In the absence of thermal fluctuations and other external forces, a single particle will be pinned at the bottom of a flashing ratchet potential under the overdamped condition. Unidirectional motion becomes possible if there exist interactions among particles. In this paper, the overdamped directed motion of a dimer with two heads in a flashing ratchet potential is investigated. We propose the mechanism to reveal how two heads of the dimer cooperate and help each other to move processively. The necessary condition of directed motion is analytically given, which is in good agreement with numerical simulation results. Furthermore, the resonant steps of the current are observed and discussed. The scenario and the results proposed in this paper may shed light on the elaborations of artificial molecular motors.

The motion of molecular motor is essential to the biophysical functioning of living cells. This motion can be regarded as a multiple chemical state process. So, mathematically, the motion of molecular motor can be described by several coupled one-dimensional hopping processes or by several coupled Fokker–Planck equations. To know the basic properties of molecular motor, in this paper, we will give detailed analysis about the simplest case in which there are only two chemical states. Actually, many of the existing models, such as the flashing ratchet model, can be regarded as a two-state model. From the explicit expression of the mean velocity, one can see that the mean velocity of molecular motor might be non-zero even if the potential in each state is periodic, which means that there is no energy input to the molecular motor in each of the two states. At the same time, the mean velocity might be zero even if there is non-trivial energy input. Generally, the velocity of molecular motor depends not only on the potentials (or corresponding forward and backward transition rates) in the two chemical states, but also on the transition rates between them.

In living cells, molecular motors convert chemical energy into mechanical work. Its thermodynamic energy efficiency, i.e. the ratio of output mechanical work to input chemical energy, is usually high. However, using two-state models, we found the motion of molecular motors is loosely coupled to the chemical cycle. Only part of the input energy can be converted into mechanical work. Others are dissipated into environment during substeps without contributions to the unidirectional movement.

Bacterial flagellar motor (BFM) is one of the ion-driven molecular machines, which drives the rotation of flagellar filaments and enable bacteria to swim in viscous solutions. Understanding its mechanism is one challenge in biophysics. Based on previous models and inspired by the idea used in description of motor proteins, in this study one two-state model is provided. Meanwhile, according to corresponding experimental data, mathematical relationship between BFM membrane voltage and pH value of the environment, and relationship between internal and external sodium concentrations are given. Therefore, with model parameter values obtained by fitting theoretical results of torque-speed relation to recent experimental data, many biophysical properties of bacterial flagellar motor can be obtained for any pH values and any external sodium concentrations, including the rotation speed, stall torque (i.e. the torque generated by BFM), rotation dispersion, and rotation randomness. In this study, the single-stator BFM will be firstly analyzed, and then properties of multiple-stator BFM are addressed briefly.

In this work, we consider a stochastic model describing the unidirectional rotation of the rotor (subunit γ) of F₁-ATPase. For appropriate choice of the model parameters, we used literature data on dynamic parameters of F₁-ATPase and results of our calculations of electrostatic interactions in enzyme-substrate complex of the catalytic cycle. The model takes into account thermal fluctuations of the bath and stochastic processes of substrate binding and product dissociation from the catalytic centers. The model provides an adequate description of ATP-driven rotations of subunit in F₁-ATPase.

Actin polymerization driven stochastic movement of the bacteria Listeria monocytogenes is often measured using single-particle tracking (SPT) methodology and analyzed in terms of statistics. Experimental results suggested a dynamic association between the growing actin filaments and the propelled bacteria. Based on an alternative mathematical formalism for a Brownian ratchet (BR), we introduce such an attractive interaction into the one-dimensional BR model and show that its effect is equivalent to an external resistant force on the bacterium. Such a force significantly reduces the Brownian motion of a driven bacterium, and accentuates the stepping due to polymerization. We then consider the growth, with and without a barrier, of a filamentous bundle consisting of N identical filaments. It is shown that the bundle grows with a similar rate as a single filament in the absence of a load, but can oppose N times the external force under the stalling condition. A set of relationships describing the velocity of the bacterium movement (V_z) and its apparent diffusivity (D_z) as functions of the resistant force (F) and the number of filaments in a bundle (N) are obtained. The theoretical study suggests methods for data analysis in future experiments with applied external resistant force.

DNA, RNA and proteins are among the most important macromolecules in a living cell. These molecules are polymerized by molecular machines. These natural nano-machines polymerize such macromolecules, adding one monomer at a time, using another linear polymer as the corresponding template. The machine utilizes input chemical energy to move along the template which also serves as a track for the movements of the machine. In the Alan Turing year 2012, it is worth pointing out that these machines are "tape-copying Turing machines". We review the operational mechanisms of the polymerizer machines and their collective behavior from the perspective of statistical physics, emphasizing their common features in spite of the crucial differences in their biological functions. We also draw the attention of the physics community to another class of modular machines that carry out a different type of template-directed polymerization. We hope this review will inspire new kinetic models for these modular machines.

F_O is a membrane-embedded part of ATP synthase, transforming proton current running within this molecule into a rotational motion taking place between two subunits, c-subunit and a-subunit. How the proton current could be transformed into the rotational motion remains unclear. In this paper, by means of molecular dynamics simulation, we studied basic properties of the rotational motion. In equilibrium, the c-ring, which consists of 10-12 c-subunits and interacts with the a-subunit, showed stepwise rotational motion. The rotational motions resulted in a free rotational diffusion in a longer period. The diffusion constant calculated as a function of temperature showed a glass-transition-like behavior: at the lower temperatures, diffusional motion was significantly suppressed, deviating from the Einstein's relation. Under a non-equilibrium condition where different heat baths with different temperatures are applied, respectively, to the c-ring and the a-subunit, we found that directionality arises in the rotational diffusion. We finally point out how the structural flexibility (i.e., softness) of protein molecules pertains to our results.